MT-1620 al.2002 El d x d2/+m=0 Also assume that El does not vary with X E (23-5) dx Placing the assumed mode in the governing equation dw E 100 I 4e mo we This gives a w E m02=0 (23-6) d x which is now an equation solely in the spatial variable(successful separation of t and x dependencies Must now find a solution for W(x) which satisfies the differential equations and the boundary conditions Note: the shape and frequency are intimately linked (through equation 23-6 Paul A Lagace @2001 Unit 23-5it it MIT - 16.20 Fall, 2002 So: 2 d 2 EI dw  + mw = 0 dx2  dx2  ˙˙ Also assume that EI does not vary with x: 4 EI ˙˙ dw + mw = 0 (23-5) dx 4 Placing the assumed mode in the governing equation: 4 EI d w e ω − mω2 w e ω = 0 dx 4 This gives: 4 EI d w − mω2 w = 0 (23-6) dx 4 which is now an equation solely in the spatial variable (successful separation of t and x dependencies) _ Must now find a solution for w(x) which satisfies the differential equations and the boundary conditions. Note: the shape and frequency are intimately linked (through equation 23-6) Paul A. Lagace © 2001 Unit 23 - 5